An object of the present invention is to provide a time-multiplexing method for a MIMO radar which permits a more accurate angle estimate.
This object is achieved according to the present invention by a method of the kind recited initially in which:
(a) the transmitted signal is frequency-modulated in ramp-shaped fashion and exhibits a modulation pattern that encompasses several sequences of ramps which follow one another within the respective sequence in time-offset fashion at a time interval,                at least two of the sequences being associated with different transmission switching states that differ in terms of the selection of antenna elements used for transmission, and being temporally interleaved with one another,        a switchover occurring, between successive ramps that are associated with different transmission switching states, between the relevant transmission switching states,        at least one of the transmission switching states respectively having associated with it at least two of the sequences that are temporally interleaved with one another and exhibit with respect to one another, with reference to a first sequence, a time offset associated with a respective further sequence;        
(b) from the baseband signals, at least for the at least one transmission switching state with which several sequences are associated, a two-dimensional spectrum is calculated separately for each of those sequences by two-dimensional Fourier transformation, transformation occurring in the first dimension ramp for ramp and transformation occurring in the second dimension over a ramp index that counts the ramps within the sequence;
(c) based on a position of a peak in at least one two-dimensional spectrum of the baseband signals, values for the relative velocity of a radar target which are periodic with a predetermined velocity period are determined,
(d) phase relationships of spectral values that are obtained respectively at the same position and respectively for the same transmission switching state in the separately calculated two-dimensional spectra are checked for agreement with phase relationships expected for several of the periodic values of the relative velocity in the context of the respective transmission switching state; and
(e) based on the result of the check, an estimated value for the relative velocity of the radar target is selected from the determined periodic values of the relative velocity.
The sequences are temporally interleaved with one another. In other words, the ramps of one sequence have ramps of the respective other sequence(s) disposed in gaps between them. The term “interleaved with one another” is used here synonymously with the terms “intermeshed with one another” or “interwoven with one another.”
An undersampling of the Doppler shift frequency occurs over the sequence of ramps, so that the information obtained regarding the relative velocity is affected by an ambiguity. In particular, the value of the relative velocity is periodic with a velocity interval
                              Δ          ⁢                                          ⁢          v                =                  c                      2            ⁢                                                  ⁢                          f              0                        ⁢                          T                              r                ⁢                                                                  ⁢                2                ⁢                                                                  ⁢                r                                                                        (        1        )            
where c is the speed of light, f0 the average transmission frequency, and Tr2r the time interval between the ramps within a sequence. An ambiguity-affected value of the relative velocity of the radar target is therefore determined from a position of a peak, associated with the radar target, in a two-dimensional spectrum of the sampled baseband signals. The ambiguity can then be resolved by investigating how well those phase relationships between the signals of the sequences associated with the same transmission switch state which are expected for the respective values of the relative velocity agree with the measured phase relationship. The expected phase relationship depends respectively on the relative velocity and on the time offset between the relevant sequences.
This allows an unambiguous estimate of the relative velocity within a velocity measuring range that can be, for example, at least a multiple of the unambiguity range of a measurement with only one of the sequences of ramps. It is advantageous in particular that relatively long time intervals are possible between the ramps, i.e., between the ramp center points, of a sequence, so that the hardware outlay is decreased or a more accurate localization is enabled for the same hardware outlay.
The particular advantage resulting from the temporal interleaving of the sequences which is thereby simplified is that the baseband signals or spectra thereof that are used for angle determination, which are obtained with different transmission switching states, are measured almost simultaneously, so that phase shifts resulting from relative motions can be minimized and/or can be corrected particularly accurately.
An improved angle estimate can thus be enabled despite decreased hardware costs due to shorter time intervals.
The ramps are preferably disposed at irregular spacings within a period of the modulation pattern whose length corresponds to the time interval Tr2r, so that the modulation pattern exhibits as little symmetry as possible despite the regular time interval Tr2r. Because of the uniform time interval Tr2r, the time offsets between the ramps of different sequences repeat from one period to another.
Preferably, in step (e) of selecting an estimated value for the relative velocity of the radar target, the estimated value for the relative velocity is unambiguously determined in a measurement range for the relative velocity, an upper maximum value vmax of the measurement range being related as follows to the temporal spacing Tr2r of the ramp center points within a sequence:Tr2r>c/(4f0vmax)
where c is the speed of light and f0 the average transmission frequency. This corresponds to an undersampling of a maximum relative velocity vmax of a radar target which is to be detected, by way of the respective sequence of ramps having the temporal spacing Tr2r between successive ramps. Preferably Tr2r is equal to at least a multiple of the aforesaid variable on the right side of the equation.
Preferably, in step (e) of selecting an estimated value for the relative velocity of the radar target, the estimated value for the relative velocity is unambiguously determined in a measurement range for the relative velocity, an upper maximum value vmax of the measurement range being related as follows to the respective time offset T12 of the respective further sequence:T12>c/(4f0vmax)
Preferably T12 is equal to at least a multiple of the aforesaid variable on the right side of the equation. The hardware outlay for carrying out the method can be reduced by selecting such a relatively large time offset T12 between the sequences of the ramps, since the resulting ambiguity of the measured phase relationship can be permitted. This is because an unambiguous estimated value for the relative velocity can nevertheless be determined within the larger measurement region.
Advantageous embodiments of the present invention are described herein.
In an angularly resolving measurement, antenna elements are disposed in various positions in a direction in which the radar sensor is angularly resolving. For example, several antenna elements are used for reception. For an ideal, approximately point-like radar target in a respective angular position, a characteristic phase relationship and amplitude relationship exists between the signals received in different antenna elements. The amplitude ratios between the received signals depend on the directional angle and on the sensitivity curves of the antenna elements. It is possible to determine the angular position of a localized radar object by evaluating the phase relationships and/or by evaluating the amplitude relationships.
For a standard object at a given distance and having a given reflection intensity, the dependence of the amplitude and phase of the signal, transmitted from one antenna element and received after reflection at the radar target at one antenna element, on the angular position of the localized radar target can be depicted in an antenna diagram. The angular position of a radar target can be determined, for example, by equalizing the amplitudes and/or phases obtained for different selections of antenna elements used for transmission and reception, with the corresponding antenna diagrams.
Preferably, successive ramps within a respective sequence have an identical ramp slope and an identical difference between their ramp center frequencies as well as, particularly preferably, an identical frequency swing, the aforesaid difference in the ramp center frequencies optionally being not equal to zero, and ramps that have the same ramp index in the respective sequences exhibiting the same ramp slope and the same ramp center frequency as well as, particularly preferably, an identical frequency swing. The phase relationships resulting from the relative velocity of a radar target can be measured particularly accurately, and angle determination is simplified, if the frequency profile of all ramps of all sequences is identical, except for the frequency difference from ramp to ramp which is optionally selected to be not equal to zero.
The available measurement time can be utilized particularly effectively if the time offset between the sequences and the temporal spacing of the ramps within a sequence are of the same order of magnitude. Influences of an object acceleration on the phase relationship between the baseband signals of the individual sequences can furthermore thereby be minimized. Favorable values for the time offset between the sequences and the temporal spacing of the ramps within a sequence, which values are as “incommensurable” as possible (i.e., for example are not multiples of one another), can furthermore thereby be selected. Resolution of the ambiguity then results in a particularly large measurement range for the relative velocity. The modulation pattern accordingly contains pauses between the ramps. In particular, the modulation pattern preferably exhibits at least one pause that recurs regularly between each two successive ramps of a sequence, with a time interval from one pause to another which is equal to the time interval between the ramps of a sequence.
Preferably, ramps of the respective sequences are disposed alternately during a predominant time span of the modulation pattern, i.e., the sequences largely overlap in time. Preferably the time offset, associated with a respective further sequence, between the ramps of the further sequence and the relevant ramps of the first sequence is less than twice the time interval between the ramps within a respective sequence, particularly preferably is less than that time interval. The latter is equivalent to saying that one respective ramp of a respective further sequence of ramps that are associated with the same transmission switching state is always transmitted between two successive ramps of a first sequence.
Preferably, the separately calculated two-dimensional spectra are merged into one two-dimensional spectrum of the baseband signals, in particular into a power spectrum, that is used in step (c) of determining values for the relative velocity. The merger is, for example, non-phase-coherent, preferably a non-phase-coherent summation of the squares of the absolute values of the spectral values to yield a power spectrum. The detection of a peak can thereby be improved. In particular, the decrease in the signal to noise ratio of the separately calculated spectra, brought about by the distribution of the available measurement time into several sequences of ramps and by the pauses, can thereby be largely compensated for.
Preferably a relationship in accordance with the equation
                              Δφ                      12            ,            m                          =                  2          ⁢          π          ⁢                      2            c                    ⁢                      f            0                    ⁢                      T                          12              ,              m                                ⁢          v                                    (        2        )            is used in the context of checking the phase relationship, which equation correlates a phase difference Δϕ12,m expected between a phase of the spectral value of the respective spectrum of a further sequence and a phase of the spectral value of the spectrum of the first sequence of the same transmission switching state m, with the time offset T12 associated with the further sequence and with the relative velocity v, where c is the speed of light and f0 the average transmission frequency. Instead of T12 and Δϕ12,m for the second sequence it is possible to write generally T1i,m or Δϕ1i,m for the i-th sequence, where i>1, of the sequences associated with the transmission switching state m.
A control vector a(v,m), dependent on the relative velocity v and optionally dependent on the transmission switching state m, according to the equation
                                          a            ⁡                          (                              v                ,                m                            )                                =                                    1                              I                                      ⁢                          ⌊                                                                    1                                                                                        M                                                                                                              e                                              2                        ⁢                        π                        ⁢                                                                                                  ⁢                        j                        ⁢                                                  2                          c                                                ⁢                                                  f                          0                                                ⁢                                                  T                                                                                    1                              ⁢                              i                                                        ,                            m                                                                          ⁢                        v                                                                                                        ⌋                                      ,                            (        3        )            is preferably used in the context of checking the phase relationship, where m designates the respective transmission switching state, l is the number of sequences, i=1, . . . , l counts the sequences, and in the i-th component of the vector T1i,m (for i>1) is the time offset, associated with the i-th sequence, with respect to the first sequence, for the sequences associated with the m-th transmission switching state. The time offset between sequences always refers to sequences that are associated with the same transmission switching state. In this notation the control vector a(v) is a column vector whose components respectively describe the expected phase difference of the i-th sequence with respect to the partial measurement of the first sequence, the expected phase difference being respectively determined as a phase of a complex exponential function. The number of components of the vector is 1. The common pre-factor is a normalization factor and is equal to 1 divided by the square root of the number 1 of sequences used. In the exponent of the exponential function, j designates the imaginary unit unless otherwise indicated.
Preferably, different time offsets T1i,m of respective further sequences with respect to the respective first sequence are used in the context of different transmission switching states m. In other words, each time offset T1h,m used for a further transmission switching state having several associated sequences, where m>1 and h=1, . . . , H, differs from each time offset T1i,1 (where i=1, . . . , 1) used for a first transmission switching state, where H is the number of sequences of the further transmission switching state which are used, and optionally differs from 1. The control vector a(v,m) thus depends on the respective time offset and thus on the respective transmission switching state.
Preferably a first and a second of the transmission switching states each have associated with them at least two of the sequences which are temporally interleaved with one another and exhibit with respect to one another, with reference to a first sequence of the respective transmission switching state, a time offset associated with a respective further sequence of the transmission switching state, different time offsets of the further sequences being used in the context of the different transmission switching states.
Preferably the baseband signals used for determining the angle are subjected to a phase correction that compensates for the phase shifts expected for the estimated value of the relative velocity.
Preferably, in the context of ramps each having the same ramp index in respective sequences in the modulation pattern, the sequential order of the transmission switching states with which the ramps are respectively associated is mixed. In other words, the sequential order deviates from the generic sequential order in which the transmission switching states occur successively with their respective associated ramps. Effects on the angle determination of an error in estimating the relative velocity can thereby be decreased. In particular, between two ramps of a sequence of the first or second transmission switching state having the same ramp index, preferably at least one ramp of a sequence of the respective other transmission switching state having the same ramp index is always transmitted.
A knowledge of the control vector a(v,m) makes it possible to create an (under suitable conditions, unambiguous) relationship between the relative velocity v of the radar target and the received complex spectral values at the position of the peak, and to infer, from the phase relationships of the received signals, the relative velocity v of the radar target. But because in practice the received signals are more or less affected by noise, the velocity cannot be exactly calculated but can only be estimated, for example with the aid of a maximum likelihood estimate.
A measurement vector is defined, for example for one reception channel n, as
                                                        a                              k                ,                l                                      ⁡                          (                              n                ,                m                            )                                =                      ⌊                                                                                                      x                      1                                        ⁡                                          (                                              n                        ,                        m                                            )                                                                                                                    M                                                                                                                        x                      I                                        ⁡                                          (                                              n                        ,                        m                                            )                                                                                            ⌋                          ,                            (        4        )            where i=1, . . . , l, in the i-th component of the vector xi(n,m) designates a complex spectral value at a position k,l of the two-dimensional spectrum of the of the sampled baseband signals of the i-th sequence of ramps of the reception channel n and of the transmission switching state m. For example, n counts the reception channels such that n=1, . . . , N for N reception channels, and m counts the transmission switching states such that m=1, . . . , M for M transmission switching states.